Representation of radiation damping by fractional time derivatives

✍ Scribed by P. Ruge; C. Trinks

• Publisher: John Wiley and Sons
• Year: 2003
• Tongue: English
• Weight: 226 KB
• Volume: 32
• Category: Article
• ISSN: 0098-8847
• DOI: 10.1002/eqe.264

✦ Synopsis

Abstract

When modelling unbounded domains, formulation of a matrix‐valued force–displacement relationship which can take radiation damping into account is of major importance. In this paper, a method to describe the dynamic stiffness by a system of fractional differential equations in the time‐domain is presented. Here, a doubly asymptotic rational approximation of the low‐frequency force–displacement relationship is used, whereas a direct interpretation of the asymptotic part as a fractional derivative is possible. The numerical solution of the corresponding system of fractional differential equations is demonstrated using the infinite beam on elastic foundation as an example. Copyright © 2003 John Wiley & Sons, Ltd.